A Lorentzian path integral contour for charged AdS black holes selects a finite subset of complex saddles via Picard-Lefschetz theory, ensuring the semiclassical sum converges at finite β.
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In a doubly holographic black hole model, the dimension of the microstate Hilbert space equals the sum of the quantum-corrected thermodynamic entropies of the left and right black holes, which equals the generalised entropy quantifying entanglement between the asymptotic boundaries.
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How to tame your (black hole) saddles: Lessons from the Lorentzian Gravitational Path Integral
A Lorentzian path integral contour for charged AdS black holes selects a finite subset of complex saddles via Picard-Lefschetz theory, ensuring the semiclassical sum converges at finite β.